Question

A standardized biological microscope has an $8.0mm$focal length objective. what focal-length eyepiece should be used to achieve a total magnification of$100x$?

Short answer

$5cm$ the focal-length eyepiece should be used to achieve a total magnification of$100x$.

Step-by-step solution

Given Information

We need to find out the focal length of the eyepiece.

Simplification

$L=160mm$

role="math" localid="1648728454541" $M=100$

$f_{obj}=8mm$

As we know that the total magnification in the microscope is:

$M=-\frac{L}{f_{obj}}\times \frac{25}{f_{eye}}$

$100=\frac{160}{8}\times \frac{25}{f_{eye}}$

$f_{eye}=\frac{20\times 25}{100}$

$f_{eye}=\frac{500}{100}$

$f_{eye}=5cm$.